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Re: OT : Approximate / fast math libraries ?



On Sat, Sep 01, 2007 at 11:23:38 +0100,
  Chris Jones <jonesc hep phy cam ac uk> wrote:
> 
> Talyor expansions are valid when your argument is 'small' i.e.
> 
> sin(x) ~ x
> tan(x) ~ x
> cos(x) ~ (1-(x)*(x)/2)
> 
> etc. only work when x is small, and the error increases as x does (since the 
> size of the truncated terms become more important). Yes you can include more 
> terms but that only allows you to go to large x before the errors explode.

Just for the record (i.e. you might already know this) you can do taylor
expansions around any point, not just the places where you get the nice
looking series. This is still a significant restriction, but in cases where
you know you will be doing all of your evaluations near a specific point,
this a possibility.


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